Circular TE{HD on {b mode filter

ABSTRACT

A circular arc polygonal type waveguide provides an excellent TEon mode filter. In a circular waveguide and/or a helix waveguide for transmission of millimeter-wave energy, the electromagnetic field of the fundamental TE01 mode converts easily to that of undesirable higher order TEon modes. This conversion is undesirable for the transmission of millimeter-wave energy. According to the invention, the undesirable TEon mode is converted purposely to a higher order TEpq mode by the present mode filter, the profile of which is slightly deformed from as compared to the perfectly accurate circular one, and said converted TEpq mode is absorbed in a conventional helix waveguide. Thus, the fundamental TE01 mode is transmitted in a waveguide without distortion.

United States Patent [1 1 Inada 1 Oct. 28, 1975 1 CIRCULAR TE MODE FILTER [75] Inventor: Koichi Inada, Sakura, Japan [22] Filed: Mar. 18, 1974 [21] Appl. No.: 452,357

[30] Foreign Application Priority Data Mar. 24, 1973 Japan.... 48-33824 Apr. 14, 1973 Japan.... 48-42505 May 18, 1973 lapan.... 48-56003 June 18, 1973 Japan 48-68529 [52] US. Cl. 333/98 M; 333/21 R; 333/95 R [51] Int. C1. H01? 3/12; HOlP 3/13; H01P 1/16 [58] Field of Search... 333/98 M, 98 R, 21 R, 21 A, 333/31 R, 31 A, 95 R Den 333/95 R Anderson et a1. 333/31 A X Primary E.\-aminer.lames W. Lawrence Assistant E \'aminerMarvin Nussbaum Attorney, Agent, or FirmArmstrong, Nikaido & Wegner 57 ABSTRACT A circular arc polygonal type waveguide provides an excellent TE mode filter. In a circular waveguide and/or a helix waveguide for transmission of millimeter-wave energy, the electromagnetic field of the fundamental TE mode converts easily to that of undesirable higher order TE modes. This conversion is undesirable for the transmission of millimeter-wave energy. According to the invention, the undesirable TE,,, mode is converted purposely to a higher order TE, mode by the present mode filter, the profile of which is slightly deformed from as compared to the perfectly accurate circular one, and said converted TE mode is absorbed in a conventional helix waveguide. Thus, the fundamental TE mode is transmitted in a waveguide without distortion.

10 Claims, 28 Drawing Figures US. Patent Oct.28, 1975 Sheet 1 of 13 3,916,355

US. Patent Oct. 28, 1975 Sheet2of13 3,916,355

U.S. Patent Oct. 28, 1975 SheetSof 13 3,916,355

Fig. 6E

2 4 16 IO l2 l2 jwOZZ US Patent- Oct.28, 1975 Sheet7of 13 3,916,355

Fig 9 C10=25.5 mm 5 =25 U.S. Patent 'Oct.28, 1975 Sheet 9 of 13 3,916,355

Fig. /4(A) Fig. /4(B) US. Patent Oct. 28, 1975 Sheet 12 of13 3,916,355

Fig. /9

0.1 50 90 Fig.

T ,T ,T ,TE 2756 01 5| 52 53 54.

(GHZ) US. Patent Oct.28, 1975 Sheet 13 of 13 3,916,355

Fig 2/ Eoz (GHZ) CIRCULAR TE MODE FILTER BACKGROUND OF THE INVENTION The present invention relates to a mode filter or a suppressor for an undesired modefor a circular waveguide for transmission of millimeter-wave energy, which involves very small loss of the TE mode and very large loss for higher modes.

The TE mode is generally utilized for the transmission of millimeter-wave energy with millimeter wavelengths (for instance 40 100 GHz) since the transmission loss of the TE mode is very small in that frequency band. In a circular waveguide with a diameter several times larger than the wavelength of the energy to be transmitted many higher modes other than the TE mode appear, since the TE mode is not a dominant or principle mode for a waveguide of the above size. A slight deformity of the circular waveguide, a corner waveguide at bend portions and/or an elastic or expansion waveguide are triggers for generation of higher TE modes. These undesirable higher TE modes should be absorbed for the TE mode transmission.

It is very difficult to eliminate unwanted TE modes since the electromagnetic field of the higher TE modes are closely similar to that of the fundamental TE mode.

Various types of TE mode filters which absorb these TE, modes have been proposed. Some of them are a distribution coupling type filter, a long slit type filter, a resonant slit type filter and a phase reverse type filter. But these types of prior mode filters have the following disadvantages: (i) Their structures are very complex, requiring high degree of manufacturing accuracy and thus are very expensive: (ii) It is difficult to obtain large inner diameters such as 51 mm and so, tapered waveguides are needed to mate and these tapers may generate other TE modes. (iii) TE mode loss is relatively large. (iv) The structures of the filters are very complicated and different from that of the waveguide line.

SUMMARY OF THE INVENTION The object of the present invention is to provide a TE mode filter which overcomes the abovementioned drawbacks.

Another object of the present invention is to provide a mode filter of simple structure which is similar to the structure of a circular'or helix waveguide.

Still another object of the present invention is to provide a mode filter of short length, with a very wide frequency band.

The above and other objects are attained by a mode filter comprising a circular waveguide of a predetermined length, the cross-section of said waveguide being almost circular but being slightly deformed by the existence of a plurality of ridges on the periphery of the waveguide, whereby the mode conversion loss in said waveguide from TE, mode (n a 2) to TE mode is much greater than that from 'IE mode to another modes.

BRIEF DESCRIPTION OF THE DRAWINGS The foregoing and other objects, features and attendant advantages of the invention will be appreciated as they become better understood by the accompanying drawings wherein;

FIG. I shows a section of a whole transmission line using the mode filter according to the present invention;

FIG. 2 and FIG. 3 show two cross sections of mode filter according to the present invention;

FIG. 4 shows a modified cross section of a mode filter according to the present invention;

FIG. 5 shows another embodiment of a structure of a mode filter according to the present invention;

FIGS. 6A through 6F show calculated curves of the characteristics of the mode filter of FIG. 5;

FIGS. 7A and 78 also show calculated curves of the characteristics of a mode filter according to the present invention;

FIG. 8 shows another cross section of a mode filter according to the present invention;

FIG. 9 shows a calculated curves for the practical design of the mode filter of FIG. 8;

FIG. 10 shows a longitudinal cross section of another embodiment of a mode filter system according to the present invention;

FIG. 11 shows calculated curves of the frequency characteristics of a mode filter according to the present invention;

FIG. 12 shows a longitudinal cross section of another mode filter system according to the present invention;

FIG. 13 shows a cross section of a mode filter system of FIG. 12;

FIG. 14(A) and FIG. 14(B) indicate electric fields of a mode filter system similar to that of FIG. 12;

FIG. 15 shows curves of attenuated characteristics of TE mode by a mode filter system of FIG. 12;

FIG. 16 through FIG. 20 show calculated curves for the practical design of a mode filter according to the present invention, and

FIG. 21 shows an experimental measured curve of a mode filter according to the present invention.

PREFERRED EMBODIMENTS FIG. 1 shows a section of a whole transmission line using the mode filter according to the present invention. In FIG. 1 reference number 10 indicates a mode filter according to the present invention, 20 indicates a helix waveguide, 30 and 30a indicate ordinary circular waveguides. The TE mode propagates in the waveguide system of FIG. 1 in the direction of the arrow, and in the waveguide 30, some undesirable modes are generated. TE TE and another higher TE, modes are converted in the mode filter 10 into TE (where n 0) modes which are absorbed in the helix waveguide 20. Accordingly, pure TE mode is provided in the succeeding circular waveguide 30a.

Since the helix waveguide 20 and circular waveguide 30 or 30a are well known in the art, the main purpose of the present invention is to provide a mode filter 10 as shown in FIG. 1.

The first embodiment of the present invention, that is, a mode filter with conductive metal walls, is described below with reference to FIGS. 2, 3 and 4.

Generally speaking, a circular waveguide with metal walls whose outline is not a perfect circle but is deformed, generates undesirable higher TE,,,, modes, from the fundamental desirable TE mode where P 0. For instance, FIG. 2 shows a cross section of a circular waveguide which is almost circular but is deformed by the existence of three mounds or ridges on its inner periphery, and is made of metal with small wall impedance. In that case. an electromagnetic field of TE (where m 1, 2, 3, is generated. Mathematically,

the TE,,,, mode couples with the TE mode in the event that there are P mounds or ridges on the inner periphery of a waveguide and the instant radius between the center ofthe waveguide and the inner surface of the waveguide a is a =a (1+ 8 cospfi). In that case. the coupling coefficient C1,," between TE,,,, and TED, is expressed below. lnrlllvml lonllvml (B1n||l BlP l where lunllv l iannini-r1 Emu) I T 1 i Blonl Bluml X fl1 "l 819ml) 'JT 1(Bim 511ml) 1 (2) Accordingly, on the condition that the desirable values ofp and l are chosen, it is possible that E (1) (n 2) is considerably smaller than E (l), and the attenuation of TE and/or TE is extremely greater than that of TE The mode filter according to the present invention is based on the above principle, the cross-section of the mode filter being almost circular but slightly deformed, and the length of the mode filter being optional.

The explanation of a mode filter for the TE mode using metal wall circular waveguide is presented below.

The mode conversion loss for the TE mode is obtained from the formula (3) as follows;

(Bum Bum-11 (3) Accordingly, in order to obtain an effective TE mode filter,

should be are, small as possible.

optimum value of p, which represents the number of mounds or ridges on the periphery of a waveguide, is determined to satisfy the above conditions. The maximum values of formulas (4) and (6) are, mathematically 2.

Further, values of [3 and B are expressed as follows.

211 2 A a T 1 (8) 211' 2 Mun-i 2 Blvm! A an where a indicates the radius of a waveguide, and the wavelength of the transmitted wave. Accordingly, in order to obtain the maximum value of formula (5), the value B B should be as small as possible. That is to say, the difference between X1021 and Xlm] should be as small as possible. The reason for this and the relationship between x and B will be apparent from formula (10) and its explanation. The values of xlmnl for TE modes are the same as radix of the differentiated bessel function, and are shown in the following Table 1.

Further, the calculated value of is shown in Table 2, where the frequency fis GHz (wavelength is 3.75 mm), the radius of a waveguide a is 25.5 mm and 8, which is the deformation rate, is 0.1.

Table 2 p nm ui oz oa TE 0.167 0.010 0.004 TE 0.016 2.694 0.030 2 TE- 0.004 0.041 12.690 TF 0.002 0.011 0.075 TF 1.202 0.036 0.010 3 TE 0.009 0.326 0.100 TE 0.003 0.022 0.447 TE 0.104 0.146 0.024 4 TE 0.006 0.080 0.651 TE 0.002 0.014 0.112 TE. 0.044 1.589 0.056 5 TE 0.005 0.037 5.756 TE 0.002 0.010 0.055 TE 0.027 3.093 0.145

Table 2-Continued p TEW" TE m IIZ TEN! TE 0.004 0.023 0.330 TE 0.019 0.365 0.509

TE 0.003 0.017 0.121 TE 0.014 0.153 5.664

TE 0.003 0.013 0.066 9 TE, 0.012 0.090 6.411 10 TE 0.010 0.062 0.840 11 TE, 0.001 0.046 0.346

The attenuation of TE TE TE modes is calculated from the above formula (3), using Tables I and 2. When p 2, the attenuation of the TE mode can be more than ten times as large as that of the TE mode, and the attenuation of the TE mode can be more than sixty times as large as that of the TE mode, therefore, a mode filter with two ridges on the periphery of the waveguide (p 2) is very beneficial. When p 3 or p 4, the attenuations of TE TE and TE are almost the same, and a mode filter of p 3 is not effective. When p 5, the attenuations of TE and TE modes are more than 30 and 110 times, respectively, as large as that of the TE mode, and a mode filter ofp is more effective than that ofp 2. When p 6, the attenuations of the TE and TE modes are more than 100 and times, respectively, as large as that of the T15 mode. When p is greater than seven, the difference of attenuation between the TE mode and higher TE, modes is considerably large and a mode filter with p greater than seven is considered effective.

On the other hand, the length l of deformed mode filter is determined to obtain the maximum value of l {(Bll" Bum-il Since the mathematical maximum value of the above formula is 2, the length I should be determined to ensure that the value of that formula is 2.

For instance, supposing that p 5, a 25.5 mm, and f= 80 GHz, then Z'rr 2 3.75

the TE mode is Said length l is obtained by the formula C03 (B1021- @1511) I: l

FIG. 3 shows the cross section of a mode filter 10 for the TE mode according to the presnet invention. Said mode filter 10 has five ridges 10a 10e. (p 5 and 8 0.05) and with a length of 840 mm the attenuation for the TE mode in 80 GHz is thirty times as large as that for the fundamental TE mode.

A post of conductive material can be used instead of a mound or a ridge on the periphery of a mode filter. FIG. 4 shows a cross-section of a post type mode filter 11, in which there is a plurality of posts l1a- 1 1e inside the wall. The function of these posts 11a lle is the same as the ridges 10a We of FIG. 3.

The second embodiment of the present mode filter 10 (FIG. 1) is described below. The second mode filter is substantially a helix waveguide, whose cross section is almost circular but is deformed by the existence of some mounds or ridges on its inner periphery.

FIG. 5 shows a structure of a helix type mode filter 12 which has an insulated helix wire 12-1, a dielectric 5 layer 12-2 of thickness t covering the outer portion of the wire 12-1 and a shield layer 12-3 shielding the outer portion of the dielectric layer 12-2. The diameters of the conductor and the insulator of the wire 12-1, are d and D, respectively. The important feature of the sec- 10 0nd embodiment of the present mode filter is that the almost circular inner surface of the wire 12-1 is deformed by the existence of some mounds or ridges. Therefore, the cross-section of the inner surface of the present helix type mode filter is similar to that of FIG. 2 or FIG. 3. The wall impedance of the helix type mode filter is designed so that the TE (n 2 2) mode is converted perfectly to the TE,,,, mode but the TE mode propagates without conversion.

Generally, the characteristic formula or equation for the particular mode in a helix waveguide or a helix mode filter is the one shown below.

3 (10) wherein e and p. represents space dielectric constant and magnetic space permeability, respectively, 34 is a propagation constant for the i mode and is expressed as 71' =ai +jBi, Zz is a wall impedance, a is an inner radius 35 of the helix waveguide, p is a number of ridges, xi is constant a is attenuation constant and B is phase constant.

From equations (9) and 10), when a), e, a and Z2 are determined, the value of xi which satisfies the above equations can be calculated easily. FIGS. 6A through 6F show the curves of the relationship between xi and jmeaZz, where the radius a of a helix waveguide is 25.5 mm, and wavelength A is 3.75 mm. Thevalue of xi ob- 0L00374/mm.

tained from these figures The value a value of the propagation constant yi through said equation (10) since a and k are constantin a particular case. In order to obtain an excellent mode filter, the difference of phase constant [3 between the undesirable mode TE, and the TE mode to be generated, sould be much smaller than the difference of the phase constant between the TE mode and the TE mode. The reason for this will be explained in detail later.

Since propagation constant 7 1' is equal to (11' +jBi and if loss factor ai is very small, the analysis of Bi can be substituted by the analysis of 'yi. Further, 7i and xi are connected by the equation (10), where values ofa and k are constant in each particular case. Accordingly, the difference of Bis depends upon the difference, of xis. That is to say, it is satisfactory that the difference of xi between the undesirable mode TE, and the TE mode to be generated is much smaller than the difference of xi between the TE,,q mode and the TE mode.

Some typical cases are presented with reference to FIGS. 6A through 6F.

a. p= 3 in FIG. 6A.

When the wall impedance Zz is designed so thatjwea- Z: is 6 (Zz is capacitive), the value of xi of the TM mode is 7.0 from FIG. 6A. And the value xi of the TE mode is 7.0 from Table 1. A helix waveguide with 3 ridges can be a T13 mode filter.

b. p 4 in FIG. 6B.

The TE mode (xi 10.17 in Table I) and TE. mode can degenerate. Thus, a helix waveguide with 4 ridges can be the T5 mode filter. That is to say, the loss of the TE mode is much larger than that of the TE mode.

c. p 5 in FIG. 6C.

When the wall impedance Z2 is designed so that jweaZz is 4 (Zz is capacitive), the value of xi of the TE, mode is the same as that of the TE mode and is equal to 7.0. Since the value of xi of the TE mode 3.8) is sufficiently different from the value of xi of 'I'E mode 7.0) the mode conversion loss of the TE mode is very small. A mode filter with five ridges is the most preferable for a TE mode filter.

d. p 6 in FIG. 6D.

Though the TE mode and the TM mode degenerate with jmeaZz being equal to I, the T mode does not couple with the TM mode in the case that the wall impedance Zz is very small such as, one. Therefore, a T13 mode filter with six ridges is not practical.

e. p 7 in FIGS. 6E.

When the wall impedance Zz is large so that the value ofjmeaZz is sufficiently inductive negative, the value of xi of the TM, mode can be equal to that of the TE mode and is equal to 10.17. Therefore, a helix waveguide with seven ridges may be a TE mode filter.

f. p= 8 in FIG. 6F

When the value ofjweaZz is 4 (Zz is capacitive), the value of xi of the TE mode is equal to that of TE mode, and is equal to 10.17. Therefore, the T13 mode is completely converted to the TE mode. A mode filter with eight ridges is the most preferable TE mode filter.

The mathematical analysis of the helix type mode filter according to the present invention is given below.

First, the amplitude of coupling coefficient Cni between the TE mode and the i mode is illustrated by the following formula. V

'yn: represents the propagation constant of TE,,,,

mode;

8: the deformation rate FIGS. 7A and 7B shows two examples of the solution of formula (11) and are curves of Cni/8 of the i mode (vertical axis) versus xi. Cni is represented as ICni/Bl along the vertical axis since the value of 8 is constant in this particular case. FIG. 7A shows the value of ICni/vSl between the TE or TE mode, and the i mode when p 5, and FIG. 7B shows the value of [Cni/8 lbetween TE or TE and the i mode when p 8. Further, in FIGS. 7A and 7B, the values of radius a and wavelength A are 25.5 mm and 3.75 mm, respectively. In FIG. 6C, when the wall impedance Zz changes from zero to the inductive direction or capacitive direction (in this figure the area above the horizontal axis is capacitive and the area under the horizontal axis is inductive), the value of xi changes to the right or left direction. Therefore, the coupling coefficient Cni changes in the direction of the arrow (inductive or capacitive) in FIG. 7A, depending upon changes of the value of xi. For instance, when the wall impedance 22 changes from zero (metal wall) to capacitive impedance in FIG. 6C, the value of xi of the TE mode approaches close to the value of xi of the TE mode (which is 7.016). Then, as in FIG. 7A, the coupling coefficients between TE and TE becomes small.

The amplitude a,-(z) of the i mode and the amplitude a (z) of TE mode in this mode filter is obtained from the following equations.

with

[7: Bni ACni where a ,(0) and a,(0) are the amplitudes of a and a with Z zero. In the case of ABoi Coi from (12) with a,-(0)=0, we get the next equation.

Cni ABm' and) l sin z 4,..(0) cm l Apr". (l cosABm'Z) When the deviation from roundness is independent of distance along the waveguide, mode conversion of the TE mode is represented by a periodic function including the term (I cos ABniL) and the maximum of a(L) becomes 2 2(Cni/ABni)? When Zz is determined, we can get the mode conversion losses of the TE mode by calculating the relation between (Cni/Afilni) E,,,,(Z)=e B on cos CniZ (l5) When Zz is set to satisfy Cni Z 1r/2, the TE mode is completely transformed into some other i mode. This i mode is absorbed easily in a conventional helix waveguide and consequently TE mode attenuations become very large.

The following describes the practical design of a helix type mode filter with five ridges (p 5) according to the present invention. In the design of a helix type mode filter, (a) the height of ridges the value of 8), (b) the length of mode filter, and (c) the structure of the wall, should be decided. Concerning the value of 8, the larger it is, the larger the coupling coefficient Cni between TE and TB becomes. That is to say, when the value of8 is large, the loss of the fundamental mode TE itself is large, thus, the upper limit of 8 is determined by the permissible attenuation of the TE mode.

Concerning the length l of the mode filter, the optimum length l is l= 1r/2 l/Cni. When the coupling coefficient Cni is large, the length I can be short. However a large coupling coefficient Cni requires a large value of 8, and results in an increased attenuation of the TE mode.

Of course, a mode filter with 1 less than 17/2 l/Cni is possible, in which case, attenuation of TE mode is reduced a little relative to the short length l.

A typical numerical example of a helix type mode filter shown in FIG. 5, where the center frequency is 80GH2, the radius of a waveguide is A 25.5 mm, the tolerable attenuation of the TE mode is 0.005 nepa, is shown below.

l= 1000 mm t=0.5 mm

d=0.l8 mm D=0.20 mm as 4(es (es is the relative dielectric constant of dieelectric layer 12-2 in FIG.

If the frequency band of the mode filter is 40 80 GHz the length I should be 750 mm. With the above numerical embodiment, the value of jweaZz holds about 5 in the whole frequency band.

Some modifications of a helix type mode filter are possible to make by those skilled in the art. For instance, a plurality of conductive paste disposed on the inner surface of a helix waveguide function in the same manner as mounds or ridges of the mode filter of FIG. 5. The helix type mode filter is, of course, used in the waveguide system shown in FIG. 1, together with an ordinary circular metal wall waveguide and an ordinary helix waveguide.

The third embodiment of the present invention concerns a dielectric lined type mode filter, the cross section of which is shown in FIG. 8. A dielectric lined type mode filter 12 comprises the deformed metal wall 12-1 and the dielectric layer 12-2 lined on the inner surface of the metal wall 12-1. The structure of dielectric lined type mode filter is the same as that of the metal wall type mode filter in FIGS. 2 and 3 except that the dielectric lined type mode filter has the dielectric layer 12-2.

The deviation of the phase constants AB and Afi for the TE mode and the TE mode, by the addition of the dielectric layer 12-2 to the metal wall are shown below.

where t is the thickness of the dielectric layer 12-2. Generally, (t/a,,) is sufficiently small, and AB is much smaller than AB Therefore, an appropriate value of (t/a provides the extremely small value of (B fl and the larger value of formula (5) (where n 2) is obtained.

FIG. 9 shows the calculated curves of the relationship between the thickness 1 of the dielectric layer (horizontal axis) and the value of (vertical axis) for the TE mode and TF mode where a, 25.5 mm and e, 2.3. It should be noted from FIG. 7 that the appropriate thickness of the dielectric layer provides the same phase constant of the TE mode as that of the TE mode, and the same phase constant of the TE mode as that of the TE mode.

The fourth embodiment of the present mode filter is described below.

FIG. 10 shows a part of a mode filter system, which comprises a first mode filter F an ordinary helix waveguide A and a second mode filter F An alternate arrangement of a mode filter F, or F and an ordinary helix waveguide A shown in FIG. 8, provides a mode filter system which covers a very wide frequency band. For instance, if the first mode filter F covers a low frequency band, such as 40 60 GHz, and the second mode filter covers a high frequency band, such as 60 80 GHz, then the whole filter system including both filters F and F covers wide frequency band 40 80 GHz. Each component filter F or F can be a helix type mode filter as illustrated by FIG. 5. The typical numerical design of a combination mode filter system shown in FIG. 10 is as follows:

Number of ridges; five (p 5) Tolerable attenuation of TE mode; 0.005 nepa Ratio of ridges; 0.04 (5= 0.04)

Radius of helix waveguide; a 25.5 mm

Frequency band; 40 80 GHz Length of first filter; L 625 mm (Center frequency is 50 GHz) Length of second filter; L 875 mm (Center frequency is GHz) Length of helix waveguide A; 1000 mm Structure of helix wall in FIG. 5

Relative dielectric constant of dielectric layer; a 4

Thickness of dielectric layer; t 32 0.5 mm

Diameter of coil; D 0.129 mm and d 0.12 mm With the above numerical design, the value OfjwaZZ of both filters F and F is about four.

In the combination mode filter system of FIG. 10, the micro-wave energy propagates in the direction of the arrow, and undesirable TE mode included in the low frequency band is converted by the first filter F, to the TF mode, which is absorbed by the helix waveguide A. Further, undesirable TE mode included in the high frequency band is converted by the second filter F to the TE mode, which is absorbed by a succeeding helix waveguide (not shown). Some modifications of FIG. 10 are, of course, possible. For instance, a metal wall type mode filter or dielectric lined type mode filter can be used as a component of a combination filter system, instead of the helix type mode filter.

With regard to the fifth embodiment of the present mode filter, FIG. 11 shows the relationship between the length (horizontal axis; cm) and the mode conversion loss of the TE mode (vertical axis; dB), with parameters of some frequencies, where radius a, 25.5 mm, number of ridges p 9, deformation rate 0.06, and the attenuation of TE mode is less than 0.1 dB. On the condition that the frequency band from 40 GHz to 90 GI-Iz should be covered by a single mode filter, the length of that filter is determined to be 12 cm from Point A in FIG. 11, and the loss of the upper limit frequency (90 GHz) is the same as that of the lower limit of frequency (40 GHz). However, with the length of 12 cm, any significant loss at both higher and lower frequencies is not satisfactory. The fourth embodiment described above with reference to FIG. 10, overcomes that disadvantage, but the mode filter in said fourth embodiment is too large in size.

Therefore, the fifth embodiment provides a wide band mode filter of a small size.

FIG. 12 and FIG. 13 show the longitudinal view and cross sectional view, respectively, of a filter system of the fifth embodiment, which comprises a first filter F, and second filter F The second filter F is connected to the first filter F, along a common longitudinal axis, however, corresponding points on the periphery of filters F, and F for instance a on F, and a on F in FIG. 13, are separated from each other by angle 6. Said angle 6 is determined as 6 2rr/4p. Accordingly to the structures in FIGS. I2 and 13, since an ordinary helix waveguide between two filters like those of FIG. is unnecessary, the entire length of the filter system is shortened.

The operational principle of the filter system in FIGS. 12 and 13 is explained with a simple example (p 32 2), shown in FIGS. 14(A) and 14( B). When the TE mode propagates in a waveguide with two ridges (p 2) shown in FIG. 14(A), said TE,,,, mode is converted to the TE mode, whose field is shown in FIG. 14(A).

On the other hand, when two filters are connected directly on the condition that first one (FIG. I4(A)) is turned by angle 6 (6 =21r/4p 45) to the second one (FIG. 14(8)), the electrical fields in FIG. 14(A) and FIG. 14(B) are in the relationship of a sine mode to a cosine mode, and those fields do not couple with each other. Accordingly, two filters of FIG. I4(A) and FIG. 14(B) operate independently and it seems as if two mode filters are provided. Therefore, an ordinary helix waveguide between two filters can be omitted.

Numerical design of the fifth embodiment is shown below.

Type of waveguide; metallic wall waveguide Number of ridges; nine (p =9) Inner radius; a 25.5 mm

Length of first filter; L, 10 cm Length of second filter; L l8 cm Deformation rate; 8 =0.06

The characteristics of the fifth embodiment with the above numerical data are shown in FIG. 15, where the horizontal axis denotes frequency in GHz and the vertical axis denotes loss of TE mode in dB, curve F, relates to the loss by first filter F, and curve F relates to the loss by second filter F As apparent from FIG. 15, the total loss F, F is almost constant between wide frequency bands.

The second numerical design of the fifth embodiment is shown below.

Type of waveguide; helix waveguide Number of ridges; p 5

Deformation rate; 6 0.04

Radius; a, 25.5 mm

Value of jweaZz; 4

Specific inductivity; a 4

Thickness of dielectric layer; I 0.5 mm

Diameters of coil; D 0.I29 mm, d 0.12 mm Length of first filter; L, 625 mm Length of second filter: L 875 mm The mode filter described in FIG. 8 is also applicable to the filter system of the fifth embodiment.

The coupling portion of first filter F, and second filter F should be covered by a metallic cover in practical use.

Next, some useful calculated data for the design of the mode filter according to the present invention are presented below.

FIG. 16 shows the relationship between jm aZz along the horizontal axis and loss factor Afini along the vertical axis on the condition that p 5, a 25.5 mm and 5 0.04. These curves are calculated from formulae (9) (10) and (11).

FIG. I7 shows the curves of the frequency in GHz along the horizontal axis versus the value of JweaZ/zon the condition that 11,, 25.5 mm, a 4, t 0.6 mm and d 0.2 mm.

FIG. I8 shows the relationship between the length of a mode filter in cm along the horizontal axis and the loss of TE mode in dB along the vertical axis with a parameter of frequencies (GHz), on the condition that p= 5 and 6 0.04. Mathematically speaking, the length l of a mode filter is determined to satisfy the formula 2 However, in the practical design in which the mode filter is used for the wide frequency band, the length I should be designed from FIG. 18 so that the losses at the highest and lowest frequencies are the same.

FIG. 19 shows the frequency characteristics of the loss of TE mode with parameters of wall impedance. In FIG. 19, the horizontal axis shows the frequency in GHz and the vertical axis shows the loss of TE mode in dB. The condition of FIG. 19 is that p 5, 8 0.04

and I cm.

FIG. 20 shows the relationship between the frequency in GHz along the horizontal axis and the loss of the fundamental TE mode in dB along the vertical axis on the condition that p 5. 6 0.04 and I 75 cm. The curve of FIG. 20 shows a total conversion loss where TE mode is converted to TE TE TE and 

1. A mode filter comprising a circular waveguide of a predetermined longitudinal length, characterized in that the cross section of said waveguide wall is almost circular but is slightly deformed by the existence of a plurality of ridges formed in the wall per se, whereby the mode conversion loss in said waveguide from the TEon mode (n > OR = 2) to the TEpm mode is much greater than that from the TE01 mode to other modes.
 2. A mode filtEr according to claim 1, further comprising a thin dielectric layer inscribed on the inner surface of said deformed waveguide.
 3. A mode filter according to claim 1, wherein the number of said ridges is six.
 4. A mode filter according to claim 1, wherein the number of said ridges is nine.
 5. A mode filter according to claim 1, wherein the number of said ridges is eight.
 6. A mode filter comprising a circular helix waveguide of a predetermined longitudinal length having at least a helix wire and a thin dielectricl layer covering said wire, characterized in that the cross section of said helix waveguide is almost circular but is slightly deformed by the existence of a plurality of ridges on the periphery of the waveguide, and that by the design of the wall impedance of said helix waveguide the difference of phase constants between the TEon mode (n > or = 2) and the converted modes from said TEon mode is smaller than the difference of phase constants between the TE01 mode and said converted modes.
 7. A mode filter according to claim 6, wherein the number of said ridges is five.
 8. A mode filter according to claim 6, wherein the number of said ridges is eight.
 9. A mode filter system comprising at least; a. a first helix waveguide having at least a helix wire and a thin dielectric layer covering said wire, the cross section of said helix waveguide is almost circular but is slightly deformed by the existence of a plurality of ridges on the periphery of the waveguide, the wall impedance of said waveguide being so designed that the difference of phase constants between the TEon mode (n > or = 2and the converted modes from said TEon is smaller than the difference of phase constants between the TE01 mode and said converted modes, the approximate length l of said helix waveguide being designated as l pi /2 .1/Cni, where Cni is the coupling coefficient between TEon mode and i mode, and the frequency characteristics of said waveguide being almost flat in the lower frequency band, b. an ordinary helix waveguide connected to said first helix waveguide, and c. a second helix waveguide connected to said ordinary helix waveguide, said second helix waveguide being similar to said first helix waveguide except that the frequency characteristics of said second helix waveguide are almost flat in the higher frequency band.
 10. A mode filter system comprising at least two circular waveguides, their cross-sections being almost circular but being slightly deformed by the existence of a plurality of ridges on the periphery of the waveguides, whereby the mode conversion loss in said waveguides from the TEon mode to the TEpm mode are much greater than that from the TE01 mode to other modes, characterized in that said two circular waveguides operate as a mode filter in lower and higher frequency bands, respectively, and that said two circular waveguides are connected along a common axis so that the corresponding points on the periphery of the two circular waveguides are separated from each other by an angle theta 2 pi /4pradian, where p is the number of said ridges along the periphery of the circular waveguides. 